1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 7b03bc34e33da4031c48262a09263a058963885a.

2 Data

Data is downloaded from the Git repository associated with [3]. This contains the daily cases and deaths reported by the NICD for South Africa by province. The data is somewhat problematic as it does not contain data by date of test or date of death but by reporting date. It’s not clear what the reporting delays are and they may be significant (especially for the deaths).

Further to the above the reporting of deaths seems to be incomplete in most provinces (see for example [4]). Furthermore reporting delays appear to be inconsistent and possibly batched making it impossible to obtain reasonable estimates for the reproduction number from these data. The exception appears to be the Western Cape where data appears to be stable (though probably not complete). Death data other than that for Western Cape is therefore excluded from this analysis.

In the case data file row 21 and 32 contain no provincial details. It is estimated by spreading the national total to the provinces in proportion to the combined mixture of the prior day and the next day.

Further fixes are applied to both case and death data:

  1. Scale up the per province data for unknown values.
  2. This results in provincial data which are not whole numbers. These are rounded to the nearest whole number.
  3. A SA column is added as the sum of the new per province data.
  4. Data is formatted and disaggregated such that item represents the incremental cases or deaths rather than cumulative figures.
  5. Data is filled with data (albeit with 0 cases or deaths) for all dates in the range.
  6. Any incremental case or death counts that are negative are set to zero.
  7. New cumulative figures are calculated.

3 Methodology

The methodology is described in detail here.

4 Results

4.1 Cases and Deaths

Below the cumulative case count is plotted by province on a log scale:

Below the cumulative reported deaths for the Western Cape is plotted on a log scale.

4.2 Current \(R_{t,m}\) estimates by Province

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Province
province Estimated Type Count (Week) Week Ending Reproduction Number [95% Confidence Interval]
EC cases 4,020 2021-01-08 0.6 [0.57 - 0.61]
FS cases 1,386 2021-01-08 0.8 [0.74 - 0.87]
GP cases 18,809 2021-01-08 0.8 [0.76 - 0.83]
KZN cases 25,324 2021-01-08 0.8 [0.79 - 0.85]
LP cases 4,865 2021-01-08 1.0 [0.92 - 1.11]
MP cases 3,291 2021-01-08 0.9 [0.87 - 1.01]
NC cases 777 2021-01-08 0.8 [0.71 - 0.84]
NW cases 2,366 2021-01-08 0.8 [0.77 - 0.88]
WC cases 14,866 2021-01-08 0.7 [0.66 - 0.69]
WC deaths 726 2021-01-08 0.8 [0.71 - 0.83]
SA cases 75,704 2021-01-08 0.8 [0.75 - 0.80]
Estimated Effective Reproduction Number by Province

Estimated Effective Reproduction Number by Province

4.3 Maps of Effective Reproduction Number

Below estimates of the reproductive number is plotted on maps of South Africa [5].

Estimated Effective Reproduction Number Based on Cases by Province

Estimated Effective Reproduction Number Based on Cases by Province

4.4 Estimated Effective Reproduction Number for South Africa over Time

Below the results for South Africa ove the last 90 days is plotted.

Estimated Effective Reproduction Number Based on Cases for South Africa over Time

Estimated Effective Reproduction Number Based on Cases for South Africa over Time

4.5 Map of Effective Reproduction Number Over Last 60 Days

Below the reproduction number by week by province is animated:

4.6 Estimated Effective Reproduction Number for Provinces over Time

The results for each province over last 90 days is plotted below.

4.6.1 Eastern Cape

Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time

Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time

4.6.2 Free State

Estimated Effective Reproduction Number Based on Cases for Free State over Time

Estimated Effective Reproduction Number Based on Cases for Free State over Time

4.6.3 Gauteng

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

4.6.4 KwaZulu-Natal

Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time

Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time

4.6.5 Limpopo

Estimated Effective Reproduction Number Based on Cases for Limpopo over Time

Estimated Effective Reproduction Number Based on Cases for Limpopo over Time

4.6.6 Mpumalanga

Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time

Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time

4.6.7 Northern Cape

Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time

Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time

4.6.8 North West

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

Estimated Effective Reproduction Number Based on Cases for Gauteng over Time

4.6.9 Western Cape

Estimated Effective Reproduction Number Based on Cases for Western Cape over Time

Estimated Effective Reproduction Number Based on Cases for Western Cape over Time

Estimated Effective Reproduction Number Based on Deaths for Western Cape over Time

Estimated Effective Reproduction Number Based on Deaths for Western Cape over Time

4.7 Detailed Results

Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.

5 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation it is believed that the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

Having said all the above it would appear that the effective reproduction number was reasonably high in South Africa from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.

6 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] V. Marivate et al., “Coronavirus disease (COVID-19) case data - South Africa.” Zenodo, 21-Mar-2020 [Online]. Available: https://zenodo.org/record/3888499. [Accessed: 26-Oct-2020]

[4] D. Bradshaw, R. Laubscher, R. Dorrington, P. Groenewald, and T. Moultrie, “Report on weekly deaths in South Africa 1 January - 1 December 2020 (Week 48),” Burden of Disease Research Unit, South African Medical Research Council, Dec. 2020 [Online]. Available: https://www.samrc.ac.za/sites/default/files/files/2020-12-09/weekly1December.pdf

[5] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018 [Online]. Available: https://data.humdata.org/dataset/south-africa-admin-level-1-boundaries